To determine the value of [tex]\( z \)[/tex] that makes the expression [tex]\( \frac{2}{z-3} \)[/tex] undefined, we need to focus on the denominator of the fraction.
In mathematics, a fraction is undefined when its denominator is equal to zero, as division by zero is not allowed.
Given the expression [tex]\( \frac{2}{z-3} \)[/tex], the denominator is [tex]\( z-3 \)[/tex].
To find the value of [tex]\( z \)[/tex] that makes the denominator zero, we set the denominator equal to zero and solve for [tex]\( z \)[/tex]:
[tex]\[
z - 3 = 0
\][/tex]
Adding 3 to both sides of the equation gives:
[tex]\[
z = 3
\][/tex]
Thus, the value of [tex]\( z \)[/tex] that makes the expression [tex]\( \frac{2}{z-3} \)[/tex] undefined is [tex]\( z = 3 \)[/tex].
